Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

Product autoregressive models for non-negative variables

When variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type Xt = Xα t−1Vt , 0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper, we study the properties of such models and propose methods for parameter estimation. Explicit solutions of the model are obtained in the case of gamma marginal distribution

Energy saving innovations, non-exhaustible sources of energy and long-run: what would happen if we run out of oil?

We formulate and solve a model of factor saving technological improvement considering three factors of production: labor, capital and energy. The productive activities have three main characteristics: first, in order to use capital goods firms need energy; second, there are two sources of energy: non-exhaustible and exhaustible; third, capital goods can be of different qualities and the quality of these goods can be changed along two dimensions -reducing the need of energy or changing the source of energy used in the production process. The economy goes through three stages of development after industrialization. In the first, firms make use of exhaustible energy and the e¢ ciency in the use of energy is constant. In the second stage, as the price of energy grows the e¢ ciency in its use is increased. In the third stage, the price of exhaustible sources is so high that firms have incentives to use non-exhaustible sources of energy. During this stage the price of energy is constant. In this set up, the end of the oil age has level effects on consumption and output but it does not cause the collapse of the economic system.

Energy Saving Innovations, Non-Exhaustible Sources of Energy and Long-Run: What Would Happen if we Run Out of Oil?

Se formula y resuelve un modelo de cambio tecnológico ahorrador de factores de producción que considera tres factores: capital, trabajo y energía. El modelo cuenta con características específicas con respecto a la interacción n entre la energía (la cual, de acuerdo a su fuente puede ser renovable y no renovable) y el capital. Una vez esta economía se ha definido, se supone que evoluciona en tres etapas luego de su industrialización, durante las cuales el carácter renovable o no renovable de la energía influye su precio relativo, eficiencia y afecta también el nivel agregado de consumo y producción de la economía, sin que esta evolución lleve al colapso del sistema económico.

A New Class of Non Negative Distributions Generated by Symmetric Distributions

In this article, we study a new class of non negative distributions generated by the symmetric distributions around zero. For the special case of the distribution generated using the normal distribution, properties like moments generating function, stochastic representation, reliability connections, and inference aspects using methods of moments and maximum likelihood are studied. Moreover, a real data set is analyzed, illustrating the fact that good fits can result.

Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

On numerical simulations of a nonlinear self-excited system with two non-ideal sources

In this work, the dynamic behavior of self-synchronization and synchronization through mechanical interactions between the nonlinear self-excited oscillating system and two non-ideal sources are examined by numerical simulations. The physical model of the system vibrating consists of a non-linear spring of Duffing type and a nonlinear damping described by Rayleigh's term. This system is additional forced by two unbalanced identical direct current motors with limited power (non-ideal excitations). The present work mathematically implements the parametric excitation described by two periodically changing stiffness of Mathieu type that are switched on/off. Copyright © 2005 by ASME.

Fossil and Non-Fossil Sources of Different Carbonaceous Fractions in Fine and Coarse Particles by Radiocarbon Measurement

Radiocarbon offers a unique possibility for unambiguous source apportionment of carbonaceous particles due to a direct distinction of non-fossil and fossil carbon. In this work, particulate matter of different size fractions was collected at 4 sites in Switzerland to examine whether fine and coarse carbonaceous particles exhibit different fossil and contemporary sources. Elemental carbon (EC) and organic carbon (OC) as well as water-soluble OC (WSOC) and water-insoluble OC (WINSOC) were separated and determined for subsequent 14C measurement. In general, both fossil and non-fossil fractions in OC and EC were found more abundant in the fine than in the coarse mode. However, a substantial fraction (~20 ± 5%) of fossil EC was found in coarse particles, which could be attributed to traffic-induced non-exhaust emissions. The contribution of biomass burning to coarse-mode EC in winter was relatively high, which is likely associated to the coating of EC with organic and/or inorganic substances emitted from intensive wood burning. Further, fossil OC (i.e. from vehicle emissions) was found to be smaller than non-fossil OC due to the presence of primary biogenic OC and/or growing in size of wood-burning OC particles during aging processes. 14C content in WSOC indicated that the second organic carbon rather stems from non-fossil precursors for all samples. Interestingly, both fossil and non-fossil WINSOC concentrations were found to be higher in fine particles than in coarse particles in winter, which is likely due to primary wood burning emissions and/or secondary formation of WINSOC.

Fossil vs. non-fossil sources of fine carbonaceous aerosols in four Chinese cities during the extreme winter haze episode of 2013

During winter 2013, extremely high concentrations (i.e., 4–20 times higher than the World Health Organization guideline) of PM2.5 (particulate matter with an aerodynamic diameter < 2.5 μm) mass concentrations (24 h samples) were found in four major cities in China including Xi'an, Beijing, Shanghai and Guangzhou. Statistical analysis of a combined data set from elemental carbon (EC), organic carbon (OC), 14C and biomass-burning marker measurements using Latin hypercube sampling allowed a quantitative source apportionment of carbonaceous aerosols. Based on 14C measurements of EC fractions (six samples each city), we found that fossil emissions from coal combustion and vehicle exhaust dominated EC with a mean contribution of 75 ± 8% across all sites. The remaining 25 ± 8% was exclusively attributed to biomass combustion, consistent with the measurements of biomass-burning markers such as anhydrosugars (levoglucosan and mannosan) and water-soluble potassium (K+). With a combination of the levoglucosan-to-mannosan and levoglucosan-to-K+ ratios, the major source of biomass burning in winter in China is suggested to be combustion of crop residues. The contribution of fossil sources to OC was highest in Beijing (58 ± 5%) and decreased from Shanghai (49 ± 2%) to Xi'an (38 ± 3%) and Guangzhou (35 ± 7%). Generally, a larger fraction of fossil OC was from secondary origins than primary sources for all sites. Non-fossil sources accounted on average for 55 ± 10 and 48 ± 9% of OC and total carbon (TC), respectively, which suggests that non-fossil emissions were very important contributors of urban carbonaceous aerosols in China. The primary biomass-burning emissions accounted for 40 ± 8, 48 ± 18, 53 ± 4 and 65 ± 26% of non-fossil OC for Xi'an, Beijing, Shanghai and Guangzhou, respectively. Other non-fossil sources excluding primary biomass burning were mainly attributed to formation of secondary organic carbon (SOC) from non-fossil precursors such as biomass-burning emissions. For each site, we also compared samples from moderately to heavily polluted days according to particulate matter mass. Despite a significant increase of the absolute mass concentrations of primary emissions from both fossil and non-fossil sources during the heavily polluted events, their relative contribution to TC was even decreased, whereas the portion of SOC was consistently increased at all sites. This observation indicates that SOC was an important fraction in the increment of carbonaceous aerosols during the haze episode in China.

bioNMF: a versatile tool for non-negative matrix factorization in biology

Medical imaging has become an absolutely essential diagnostic tool for clinical practices; at present, pathologies can be detected with an earliness never before known. Its use has not only been relegated to the field of radiology but also, increasingly, to computer-based imaging processes prior to surgery. Motion analysis, in particular, plays an important role in analyzing activities or behaviors of live objects in medicine. This short paper presents several low-cost hardware implementation approaches for the new generation of tablets and/or smartphones for estimating motion compensation and segmentation in medical images. These systems have been optimized for breast cancer diagnosis using magnetic resonance imaging technology with several advantages over traditional X-ray mammography, for example, obtaining patient information during a short period. This paper also addresses the challenge of offering a medical tool that runs on widespread portable devices, both on tablets and/or smartphones to aid in patient diagnostics.

Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours.